Firstly, there is no order in place preventing you from going to her home or having contact - if there was, it would have had to have been served on you before it was effective. Therefore, if you have not been served with such an order, there isn't one in place.
As there is no child arrangements order in place, you will need to get one before you can enforce contact. You need to apply on form C100, the cost of which is £215, unless you are on a low income or benefits in which case you may be entitled to fee remission - see form EX160.
You will also need to attend a MIAM - mediation information and assessment meeting, though it is likely your ex will refuse to engage if she is claiming there is an order preventing you having contact. Nonetheless, as you will see from the C100 form there is a requirement for you to attend a MIAM unless you meet one of the exeptions.
There isn't, unfortunately, a quicker way for you to regain contact with your children - court is really your way forward at this juncture, particularly since she is claiming there is an order against you (can't be if it hasn't been served on you).